# tan, tanf, tanl

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< c‎ | numeric‎ | math

Defined in header ``<math.h>`` |  |
float tanf( float arg ); | (1) | (since C99)
double tan( double arg ); | (2) |
long double tanl( long double arg ); | (3) | (since C99)
_Decimal32 tand32( _Decimal32 arg ); | (4) | (since C23)
_Decimal64 tand64( _Decimal64 arg ); | (5) | (since C23)
_Decimal128 tand128( _Decimal128 arg ); | (6) | (since C23)
Defined in header ``<tgmath.h>`` |  |
#define tan( arg ) | (7) | (since C99)

1-6) Computes the tangent of arg (measured in radians).
7) Type-generic macro: If the argument has type long double, (3) (`tanl`) is called. Otherwise, if the argument has integer type or the type double, (2) (`tan`) is called. Otherwise, (1) (`tanf`) is called. If the argument is complex, then the macro invokes the corresponding complex function (ctanf, ctan, ctanl).

The functions (4-6) are declared if and only if the implementation predefines `__STDC_IEC_60559_DFP__` (i.e. the implementation supports decimal floating-point numbers). | (since C23)

### Parameters

arg | - | floating-point value representing angle in radians

### Return value

If no errors occur, the tangent of arg (tan(arg)) is returned.

The result may have little or no significance if the magnitude of arg is large. | (until C99)

If a domain error occurs, an implementation-defined value is returned (NaN where supported).

If a range error occurs due to underflow, the correct result (after rounding) is returned.

### Error handling

Errors are reported as specified in `math_errhandling`.

If the implementation supports IEEE floating-point arithmetic (IEC 60559):

- if the argument is ±0, it is returned unmodified;
- if the argument is ±∞, NaN is returned and FE_INVALID is raised;
- if the argument is NaN, NaN is returned.

### Notes

The case where the argument is infinite is not specified to be a domain error in C, but it is defined as a domain error in POSIX.

The function has mathematical poles at π(1/2 + n); however no common floating-point representation is able to represent `π/2` exactly, thus there is no value of the argument for which a pole error occurs.

### Example

Run this code

    #include <errno.h>
    #include <fenv.h>
    #include <math.h>
    #include <stdio.h>

    #ifndef __GNUC__
    #pragma STDC FENV_ACCESS ON
    #endif

    int main(void)
    {
        const double pi = acos(-1);

        // typical usage
        printf("tan(pi*1/4) = %+f\n", tan(pi * 1 / 4)); //   45 deg
        printf("tan(pi*3/4) = %+f\n", tan(pi * 3 / 4)); //  135 deg
        printf("tan(pi*5/4) = %+f\n", tan(pi * 5 / 4)); // -135 deg
        printf("tan(pi*7/4) = %+f\n", tan(pi * 7 / 4)); //  -45 deg

        // special values
        printf("tan(+0) = %f\n", tan(0.0));
        printf("tan(-0) = %f\n", tan(-0.0));

        // error handling
        feclearexcept(FE_ALL_EXCEPT);
        printf("tan(INFINITY) = %f\n", tan(INFINITY));
        if (fetestexcept(FE_INVALID))
            puts("    FE_INVALID raised");
    }

Possible output:

    tan(pi*1/4) = +1.000000
    tan(pi*3/4) = -1.000000
    tan(pi*5/4) = +1.000000
    tan(pi*7/4) = -1.000000
    tan(+0) = 0.000000
    tan(-0) = -0.000000
    tan(INFINITY) = -nan
        FE_INVALID raised

### References

- C23 standard (ISO/IEC 9899:2024):

  - 7.12.4.7 The tan functions (p: TBD)

  - 7.25 Type-generic math <tgmath.h> (p: TBD)

  - F.10.1.7 The tan functions (p: TBD)

- C17 standard (ISO/IEC 9899:2018):

  - 7.12.4.7 The tan functions (p: 175)

  - 7.25 Type-generic math <tgmath.h> (p: 272-273)

  - F.10.1.7 The tan functions (p: 378)

- C11 standard (ISO/IEC 9899:2011):

  - 7.12.4.7 The tan functions (p: 240)

  - 7.25 Type-generic math <tgmath.h> (p: 373-375)

  - F.10.1.7 The tan functions (p: 519)

- C99 standard (ISO/IEC 9899:1999):

  - 7.12.4.7 The tan functions (p: 220)

  - 7.22 Type-generic math <tgmath.h> (p: 335-337)

  - F.9.1.7 The tan functions (p: 457)

- C89/C90 standard (ISO/IEC 9899:1990):

  - 4.5.2.7 The tan function

### See also

sinsinfsinl (C99)(C99) | computes sine (\({\small\sin{x} }\)sin(x)) (function)
coscosfcosl (C99)(C99) | computes cosine (\({\small\cos{x} }\)cos(x)) (function)
atanatanfatanl (C99)(C99) | computes arc tangent (\({\small\arctan{x} }\)arctan(x)) (function)
ctanctanfctanl (C99)(C99)(C99) | computes the complex tangent (function)
C++ documentation for tan

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